|
%I #9 Mar 31 2018 09:17:40
%S 0,0,1,2,0,4,0,3,1,1,0,11,0,2,1,4,0,8,0,6,1,2,0,18,0,1,1,6,0,25,0,5,1,
%T 2,0,21,0,1,1,11,0,25,0,5,1,0,0,27,0,4,1,5,0,13,0,11,1,0,0,83,0,1,1,7,
%U 0,17,0,7,1,11,0,34,0,1,1,7,0,15,0,17,1,2,0,71,0,1,1,7,0,66,0,6,1,0,0,36
%N Number of primes of the form f(n) - 1, where f(n) is the product of one or more divisors of n.
%H Alois P. Heinz, <a href="/A119607/b119607.txt">Table of n, a(n) for n = 1..2000</a>
%e The divisors of 4 are D = {1, 2, 4} and the subsets of D are {{}, {1}, {2}, {4}, {1, 2}, {1, 4}, {2, 4}, {1, 2, 4}}. Taking the product of elements in these subsets and subtracting 1 yields {-1, 0, 1, 3, 1, 3, 7, 7}, of which the primes are {3, 7}.
%t Do[l = Subsets[Divisors[n]]; l = Union[Map[Times @@ # - 1&, l]]; Print[Length[Select[l, PrimeQ]]], {n, 100}]
%t Table[Count[Union[Times@@@Subsets[Divisors[n]]]-1,_?PrimeQ],{n,100}] (* _Harvey P. Dale_, Mar 31 2018 *)
%Y Cf. A084419.
%K nonn
%O 1,4
%A _Ryan Propper_, Jun 04 2006
|
